Here’s how big a rock you’d have to drop into the ocean to see the rise in sea level happening now

During a hearing of the House Committee on Science, Space, and Technology on Wednesday, Rep Mo Brooks (R-Ala.) pressed Philip Duffy, president of Woods Hole Research Center, to identify reasons that sea levels might be rising.

They are rising, without dispute, at an estimated rate of 3.3 millimeters a year. Much of that increase is attributed by scientists to melting surface ice. The planet loses tens of billions of tons of ice each year. Enough is lost from Antarctica alone to increase global sea levels by a millimeter every three years, but that figure isn’t steady. Sea level rise is occurring at an increasing rate.

Brooks asked Duffy what else might be contributing to that rise. Duffy pointed to ground subsidence, which is the sinking of the ground in places that can exacerbate the problem of rising sea levels. Cities like New Orleans are sinking quickly, even faster in many places than the seas are rising.

Brooks asked if any other factors were contributing to sea level rise.

“Those are all that I know of,” Duffy replied.

“What about erosion!” Brooks exclaimed. “Every single year that we’re on Earth, you have huge tons of silt deposited by the Mississippi River, by the Amazon River, by the Nile, by every major river system — and for that matter, creek, all the way down to the smallest systems. And every time you have that soil or rock whatever it is that is deposited into the seas, that forces the sea levels to rise. Because now you’ve got less space in those oceans because the bottom is moving up.”

“I’m pretty sure that’s …” Duffy tried to interject.

“What about the white cliffs of Dover?” Brooks continued. “California, where you have the waves crashing against the shorelines and time and time again you have the cliffs crash into the sea. All of that displaces the water which forces it to rise, does it not?”

Brooks has a vision in his head like the classic experiment by Archimedes, in which the scientist sank down into his bath and noticed the water overflow — providing a way to determine the volume of his body. But the amount of water displaced by even a giant boulder falling into the ocean is not like a body going into a bathtub. It is, as Duffy said, minuscule.

Certainly 3.3 millimeters doesn’t sound like a lot of water to displace, and it does seem, to Brooks’s point, that it’s an amount — about 0.1 inch — that would be easy to displace with a cliff collapse near San Diego. The equivalent rise relative to surface area in an Olympic-sized swimming pool would be 0.0000000000114 millimeters. That’s not possible, though, since a water molecule isn’t that small.

We know from Archimedes’ work that the amount of earth required to displace that much water is the same volume: 1.19 trillion cubic meters. Here’s a corny video by a science teacher showing how it works.

So to make the oceans rise 3.3 millimeters, we would need to displace that 1.2 trillion cubic meters of water upward by dropping in 1.2 trillion cubic meters of dirt or stone or whatever.

How much is that? It’s a sphere of earth a bit over 8 miles in diameter. If we were to balance it at the top of the Capitol building, it would look like this.

(Google Earth)

If the sphere were stone, it would weigh about 6.6 quadrillion pounds. Just drop that in the ocean and — bloop! — 3.3 millimeters of sea-level increase. (We’re ignoring here that dropping it in some parts of the ocean would result in a mountain in that location. For the sake of explaining things, we’re pretending that the oceans are just one big uniform pool of water and that the sea level rise is similarly consistent. This isn’t how it works, of course.)

Put another way, it’s a volume of earth equivalent to taking the top five inches of every one of the United States’ 9.1 million square miles of land area and using it to coat the bottom of the world’s oceans. That would push sea levels up by 3.3 millimeters.

But, remember: That sea level rise happens annually. So every year, we’d need to take the top five inches of the United States, roll it in a ball and drop it in the ocean to get the sort of sea level rise we’re currently seeing. Don’t worry, though; assuming that the depth of Earth’s crust is about 40 kilometers in the United States, it would take 309,000 years for us to get to the mantle.

Except, of course, that sea level rise is occurring at an increasing rate. If someone could check on the white cliffs of Dover for us, we’d appreciate it.